Question

find the ratios in what the line segment joining point a (3, - 6 )and B (5,3) is divided by x-axis

Answer 1

I hope this helps...

Answer 2

Answer:

The ratio is 2:1

Step-by-step explanation:

Given: The line segment joining the points $A(x_1,y_1)=(3,-6)$ and point $B(x_2,y_2)=(5,3)$  is divided by x-axis.

To find : The ratio in which the line segment divides

Solution :

Let the point $P(x_3,y_3)$ divides the line segment in the ratio k:1

The point P lies on the x-axis i.e, y-coordinate is 0

Then, Using section formula $(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}$  

$(x,0)=(\frac{2(1)+6k}{k+1}),(\frac{(-6(1)+3k)}{k+1})$  

$(x,0)=(\frac{2+6k}{k+1}),(\frac{(-6+3k)}{k+1})$  

Equating y-coordinate

$0=\frac{(-6+3k)}{k+1}$  

$0=-6+3k$  

$3k=6$  

$k=\frac{6}{3}$  

$k=2$  

The ratio it divides is k:1=2:1